Recent content by Einstein's Cat

if b is greater than 2, say 3, then a= 3a - 3. no integer satisfies this from 1 to 10 and has a gets bigger the 3 is a smaller proportion of a so it can be assumed that this is the case

what pairs of integers satisfy that? I can't for the life of me think of any!

it would be that b= a / (a - 1) thus b has to be a multiple of a - 1 I assume that the other solution is a=b=0

There is the equation ab = a + b (the solutions have to be integers) A solution to this is a= b= 2. What are other solutions? Are there other solutions?

With the lonely runner conjecture, can the runners run along a circular track of any diameter or does the conjecture require that they run along a unit circle?

All is well

I can represent each length between points like this for k= 3 (each pair of integers represents the length between the points that are labelled such) 1, 2 1,3 2,3 for k= 4: 1,2 1,3 1,4 2,3 2,4 3,4 for k= 5 1,2 1,3 1,4 1,5 2,3 2,4 2,5 3,4 3,5 4,5

Say that there lies k points upon a straight line. My question is this: what is the total amount of lengths between these points? To elaborate, say k is 2; there are two points and so there is only one length between the two points. How many lengths would there be with k > 2? What is the...

Here is the Wikipedia article on the lonely runner conjecture https://en.m.wikipedia.org/wiki/Lonely_runner_conjecture# I have some inquires about it. Firstly I am right in thinking that "pair wise distinct" means that the speed of all runners are different? Also does every runner have to be...

Yet say in the plane there are two points, a and b (or two complex numbers) and they are both points on the same line. Could not one say that the point further from another point on the line (point c) towards the positive quadrant is greater than the other point? Analogous to the point (6,6)...

I am under the impression that the following cannot be stated, a < b, if the a term is a complex number and the b term is either a natural number or a complex number, or any other type of number for that matter. Firstly am I correct? Secondly, if I am, does there exist a theorem of some sort...

What is information?

I apologise for I am unable to express what I mean; this thread serves no purpose

I think that as this applies to any number; the solutions is any number and therefore the equation is undefined.

Let's say there's an equation 0 = √x - √x I intend to make x the subject of the equation; however because it is a square root, there are numerous solutions; however can I just assume that 0= √x - -√x= 2√x Can I now just rearrange this equation to make x the subject? In other words is the...